The first approach we adopt directly uses the theory-agnostic constraints on a -1PN deviation, and it was originally obtained in Ref. [1]}.
We use in this analysis a generalization of the tidal, aligned-spin \(\texttt {SEOBNRT}\)  [2]}, [3]}, [4]} waveform model in which the -1PN term is parameterized by the deviation parameter \(\delta \hat{\varphi }_{-2}\) .
By assuming a particular NS EOS, we can use the polynomial fit in Table REF  in conjunction with Eq. (REF ) to map a measured value of \(\delta \hat{\varphi }_{-2}\)  to an inferred value on \(\alpha _0\) ; schematically, this mapping takes the form \(\alpha _0 ( \delta \hat{\varphi }_{-2}, m_1, m_2; \text{EOS})\) .
Note that this mapping is infeasible using the multivariate fit in Table REF  because of the nonlinear dependence of \(\alpha _i\)  on \(\alpha _0\) .
Though the exact NS EOS remains unknown, we can repeat this analysis for the three candidate EOSs detailed earlier, and then use the variance on the bounds of \(\alpha _0\) , recovered each time, as an estimate of the systematic error arising from our ignorance of the true NS EOS.
